Search: id:A132414
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%I A132414
%S A132414 1,0,3,4,75
%V A132414 -1,0,3,4,75
%N A132414 Natural integers n such that n^3 - (n + 2)^2 + n + 4 is a square.
%C A132414 n^3 - (n + 2)^2 + n + 4 = n^3 - n^2 - 3*n. The set of x values of integral 
               solutions to the elliptic curve y^2 = n^3 - n^2 - 3*n (see MAGMA 
               program) is {-1, 0, 3, 4, 75}. - Klaus Brockhaus, Nov 13 2007
%e A132414 0^3 - 2^2 + 4 = 0^2, 3^3 - 5^2 + 7 = 3^2, 4^3 - 6^2 + 8 = 6^2 and 75^3 
               - 77^2 + 79 = 645^2.
%o A132414 (MAGMA) P<n> := PolynomialRing(Integers()); {x: x in Sort([ p[1] : p 
               in IntegralPoints(EllipticCurve(n^3 - n^2 - 3*n)) ])}; /* Klaus Brockhaus, 
               Nov 13 2007 */
%Y A132414 Cf. A028560, A005563.
%Y A132414 Sequence in context: A052323 A012087 A012194 this_sequence A041171 A111799 
               A135237
%Y A132414 Adjacent sequences: A132411 A132412 A132413 this_sequence A132415 A132416 
               A132417
%K A132414 sign,fini,full
%O A132414 1,3
%A A132414 Mohamed Bouhamida (bhmd95(AT)yahoo.fr), Nov 12 2007

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